On Artinian rings whose indecomposable projectives are distributive (Q1065120)

A ring R is called right locally distributive (right LD) if it is right artinian and every projective indecomposable right R-module is distributive. The class of right LD-rings is studied in this note with the primary purpose being to construct several examples of right LD- algebras. The main result shows that for a right artinian ring R, R is right LD iff given any primitive idempotents e and f, eRf is a uniserial right fRf-module iff every submodule of a projective indecomposable right R-module eR is characteristic and the lattice of two sided ideals is distributive.